Answer: (a)(i) \(6720\). (a)(ii) \(2520\). (b) \(50\).

(a)(i) We choose and arrange 5 digits from 8 digits, with no repetition:

\({}^8P_5=8\times7\times6\times5\times4=6720.\)

(a)(ii) For the number to be greater than \(60000\), the first digit must be \(6\), \(7\), or \(8\). There are 3 choices for the first digit.

After that, 4 further digits must be arranged from the remaining 7 digits:

\({}^7P_4=7\times6\times5\times4=840.\)

Therefore the number of such 5-digit numbers is

\(3\times840=2520.\)

(b) A team with at least 2 women has either 2 women and 1 man, or 3 women.

The number with 2 women and 1 man is

\(\binom52\binom41=10\times4=40.\)

The number with 3 women is

\(\binom53=10.\)

So the total number of teams is

\(40+10=\boxed{50}.\)